LMFDB - Embedded newform 2001.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.312617.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - x - 3 $ x^5 - 2x^4 - 5x^3 + 11*x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.28064$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50612 q^{2} -1.00000 q^{3} +4.28064 q^{4} -2.73973 q^{5} +2.50612 q^{6} -1.54091 q^{7} -5.71555 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.50612 q^{2} -1.00000 q^{3} +4.28064 q^{4} -2.73973 q^{5} +2.50612 q^{6} -1.54091 q^{7} -5.71555 q^{8} +1.00000 q^{9} +6.86609 q^{10} -1.30482 q^{11} -4.28064 q^{12} +3.43491 q^{13} +3.86170 q^{14} +2.73973 q^{15} +5.76257 q^{16} -2.28064 q^{17} -2.50612 q^{18} -2.39036 q^{19} -11.7278 q^{20} +1.54091 q^{21} +3.27003 q^{22} +1.00000 q^{23} +5.71555 q^{24} +2.50612 q^{25} -8.60830 q^{26} -1.00000 q^{27} -6.59606 q^{28} +1.00000 q^{29} -6.86609 q^{30} +2.47133 q^{31} -3.01060 q^{32} +1.30482 q^{33} +5.71555 q^{34} +4.22167 q^{35} +4.28064 q^{36} +10.3035 q^{37} +5.99053 q^{38} -3.43491 q^{39} +15.6591 q^{40} -3.81467 q^{41} -3.86170 q^{42} +4.29040 q^{43} -5.58545 q^{44} -2.73973 q^{45} -2.50612 q^{46} +10.4725 q^{47} -5.76257 q^{48} -4.62561 q^{49} -6.28064 q^{50} +2.28064 q^{51} +14.7036 q^{52} -0.703308 q^{53} +2.50612 q^{54} +3.57485 q^{55} +8.80712 q^{56} +2.39036 q^{57} -2.50612 q^{58} -14.9155 q^{59} +11.7278 q^{60} -0.0657559 q^{61} -6.19346 q^{62} -1.54091 q^{63} -3.98021 q^{64} -9.41073 q^{65} -3.27003 q^{66} -0.500088 q^{67} -9.76257 q^{68} -1.00000 q^{69} -10.5800 q^{70} -0.422671 q^{71} -5.71555 q^{72} +11.1034 q^{73} -25.8218 q^{74} -2.50612 q^{75} -10.2323 q^{76} +2.01060 q^{77} +8.60830 q^{78} -2.63000 q^{79} -15.7879 q^{80} +1.00000 q^{81} +9.56002 q^{82} +15.9522 q^{83} +6.59606 q^{84} +6.24833 q^{85} -10.7523 q^{86} -1.00000 q^{87} +7.45775 q^{88} +15.8300 q^{89} +6.86609 q^{90} -5.29288 q^{91} +4.28064 q^{92} -2.47133 q^{93} -26.2453 q^{94} +6.54895 q^{95} +3.01060 q^{96} +3.71639 q^{97} +11.5923 q^{98} -1.30482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} + 9 q^{10} - 8 q^{11} - 8 q^{12} + 5 q^{13} - 2 q^{14} + 3 q^{15} - 10 q^{16} + 2 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{21} + 10 q^{22} + 5 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{26} - 5 q^{27} - 14 q^{28} + 5 q^{29} - 9 q^{30} - 6 q^{31} - 8 q^{32} + 8 q^{33} + 3 q^{34} - 15 q^{35} + 8 q^{36} + 10 q^{37} - 10 q^{38} - 5 q^{39} + 26 q^{40} - 11 q^{41} + 2 q^{42} - 9 q^{43} - 16 q^{44} - 3 q^{45} - 2 q^{46} - 13 q^{47} + 10 q^{48} - 6 q^{49} - 18 q^{50} - 2 q^{51} + 12 q^{52} + q^{53} + 2 q^{54} + 13 q^{55} - 4 q^{56} + 9 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{60} + 23 q^{61} - 36 q^{62} - 5 q^{63} - q^{64} - 20 q^{65} - 10 q^{66} - 10 q^{67} - 10 q^{68} - 5 q^{69} - 16 q^{70} - 11 q^{71} - 3 q^{72} + 31 q^{73} - 18 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} + 3 q^{78} + 8 q^{79} - 8 q^{80} + 5 q^{81} + 16 q^{82} + 7 q^{83} + 14 q^{84} + 6 q^{85} - 36 q^{86} - 5 q^{87} - 3 q^{88} + 3 q^{89} + 9 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} - 39 q^{94} - 11 q^{95} + 8 q^{96} + 3 q^{97} + 38 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 + 9 * q^10 - 8 * q^11 - 8 * q^12 + 5 * q^13 - 2 * q^14 + 3 * q^15 - 10 * q^16 + 2 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^21 + 10 * q^22 + 5 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^26 - 5 * q^27 - 14 * q^28 + 5 * q^29 - 9 * q^30 - 6 * q^31 - 8 * q^32 + 8 * q^33 + 3 * q^34 - 15 * q^35 + 8 * q^36 + 10 * q^37 - 10 * q^38 - 5 * q^39 + 26 * q^40 - 11 * q^41 + 2 * q^42 - 9 * q^43 - 16 * q^44 - 3 * q^45 - 2 * q^46 - 13 * q^47 + 10 * q^48 - 6 * q^49 - 18 * q^50 - 2 * q^51 + 12 * q^52 + q^53 + 2 * q^54 + 13 * q^55 - 4 * q^56 + 9 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^60 + 23 * q^61 - 36 * q^62 - 5 * q^63 - q^64 - 20 * q^65 - 10 * q^66 - 10 * q^67 - 10 * q^68 - 5 * q^69 - 16 * q^70 - 11 * q^71 - 3 * q^72 + 31 * q^73 - 18 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 + 3 * q^78 + 8 * q^79 - 8 * q^80 + 5 * q^81 + 16 * q^82 + 7 * q^83 + 14 * q^84 + 6 * q^85 - 36 * q^86 - 5 * q^87 - 3 * q^88 + 3 * q^89 + 9 * q^90 + 8 * q^91 + 8 * q^92 + 6 * q^93 - 39 * q^94 - 11 * q^95 + 8 * q^96 + 3 * q^97 + 38 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.50612	−1.77209	−0.886047	−	0.463595i	$-0.846559\pi$
$2$	−2.50612	−1.77209	−0.886047	+	0.463595i	$0.846559\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.28064	2.14032
$5$	−2.73973	−1.22524	−0.612622	−	0.790376i	$-0.709885\pi$
$5$	−2.73973	−1.22524	−0.612622	+	0.790376i	$0.709885\pi$
$6$	2.50612	1.02312
$7$	−1.54091	−0.582408	−0.291204	−	0.956661i	$-0.594056\pi$
$7$	−1.54091	−0.582408	−0.291204	+	0.956661i	$0.594056\pi$
$8$	−5.71555	−2.02075
$9$	1.00000	0.333333
$10$	6.86609	2.17125
$11$	−1.30482	−0.393418	−0.196709	−	0.980462i	$-0.563025\pi$
$11$	−1.30482	−0.393418	−0.196709	+	0.980462i	$0.563025\pi$
$12$	−4.28064	−1.23571
$13$	3.43491	0.952673	0.476336	−	0.879263i	$-0.341964\pi$
$13$	3.43491	0.952673	0.476336	+	0.879263i	$0.341964\pi$
$14$	3.86170	1.03208
$15$	2.73973	0.707395
$16$	5.76257	1.44064
$17$	−2.28064	−0.553135	−0.276568	−	0.960994i	$-0.589197\pi$
$17$	−2.28064	−0.553135	−0.276568	+	0.960994i	$0.589197\pi$
$18$	−2.50612	−0.590698
$19$	−2.39036	−0.548387	−0.274193	−	0.961675i	$-0.588411\pi$
$19$	−2.39036	−0.548387	−0.274193	+	0.961675i	$0.588411\pi$
$20$	−11.7278	−2.62241
$21$	1.54091	0.336253
$22$	3.27003	0.697173
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	5.71555	1.16668
$25$	2.50612	0.501224
$26$	−8.60830	−1.68823
$27$	−1.00000	−0.192450
$28$	−6.59606	−1.24654
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−6.86609	−1.25357
$31$	2.47133	0.443865	0.221932	−	0.975062i	$-0.428764\pi$
$31$	2.47133	0.443865	0.221932	+	0.975062i	$0.428764\pi$
$32$	−3.01060	−0.532205
$33$	1.30482	0.227140
$34$	5.71555	0.980208
$35$	4.22167	0.713592
$36$	4.28064	0.713439
$37$	10.3035	1.69388	0.846941	−	0.531687i	$-0.178442\pi$
$37$	10.3035	1.69388	0.846941	+	0.531687i	$0.178442\pi$
$38$	5.99053	0.971793
$39$	−3.43491	−0.550026
$40$	15.6591	2.47591
$41$	−3.81467	−0.595751	−0.297876	−	0.954605i	$-0.596278\pi$
$41$	−3.81467	−0.595751	−0.297876	+	0.954605i	$0.596278\pi$
$42$	−3.86170	−0.595873
$43$	4.29040	0.654280	0.327140	−	0.944976i	$-0.393915\pi$
$43$	4.29040	0.654280	0.327140	+	0.944976i	$0.393915\pi$
$44$	−5.58545	−0.842039
$45$	−2.73973	−0.408415
$46$	−2.50612	−0.369507
$47$	10.4725	1.52757	0.763783	−	0.645473i	$-0.223340\pi$
$47$	10.4725	1.52757	0.763783	+	0.645473i	$0.223340\pi$
$48$	−5.76257	−0.831756
$49$	−4.62561	−0.660801
$50$	−6.28064	−0.888216
$51$	2.28064	0.319353
$52$	14.7036	2.03902
$53$	−0.703308	−0.0966067	−0.0483034	−	0.998833i	$-0.515381\pi$
$53$	−0.703308	−0.0966067	−0.0483034	+	0.998833i	$0.515381\pi$
$54$	2.50612	0.341040
$55$	3.57485	0.482033
$56$	8.80712	1.17690
$57$	2.39036	0.316611
$58$	−2.50612	−0.329070
$59$	−14.9155	−1.94183	−0.970917	−	0.239417i	$-0.923044\pi$
$59$	−14.9155	−1.94183	−0.970917	+	0.239417i	$0.923044\pi$
$60$	11.7278	1.51405
$61$	−0.0657559	−0.00841919	−0.00420959	−	0.999991i	$-0.501340\pi$
$61$	−0.0657559	−0.00841919	−0.00420959	+	0.999991i	$0.501340\pi$
$62$	−6.19346	−0.786570
$63$	−1.54091	−0.194136
$64$	−3.98021	−0.497527
$65$	−9.41073	−1.16726
$66$	−3.27003	−0.402513
$67$	−0.500088	−0.0610955	−0.0305477	−	0.999533i	$-0.509725\pi$
$67$	−0.500088	−0.0610955	−0.0305477	+	0.999533i	$0.509725\pi$
$68$	−9.76257	−1.18389
$69$	−1.00000	−0.120386
$70$	−10.5800	−1.26455
$71$	−0.422671	−0.0501619	−0.0250809	−	0.999685i	$-0.507984\pi$
$71$	−0.422671	−0.0501619	−0.0250809	+	0.999685i	$0.507984\pi$
$72$	−5.71555	−0.673584
$73$	11.1034	1.29956	0.649779	−	0.760123i	$-0.274861\pi$
$73$	11.1034	1.29956	0.649779	+	0.760123i	$0.274861\pi$
$74$	−25.8218	−3.00172
$75$	−2.50612	−0.289382
$76$	−10.2323	−1.17372
$77$	2.01060	0.229130
$78$	8.60830	0.974698
$79$	−2.63000	−0.295899	−0.147949	−	0.988995i	$-0.547267\pi$
$79$	−2.63000	−0.295899	−0.147949	+	0.988995i	$0.547267\pi$
$80$	−15.7879	−1.76514
$81$	1.00000	0.111111
$82$	9.56002	1.05573
$83$	15.9522	1.75098	0.875491	−	0.483234i	$-0.160538\pi$
$83$	15.9522	1.75098	0.875491	+	0.483234i	$0.160538\pi$
$84$	6.59606	0.719689
$85$	6.24833	0.677726
$86$	−10.7523	−1.15945
$87$	−1.00000	−0.107211
$88$	7.45775	0.794999
$89$	15.8300	1.67797	0.838986	−	0.544152i	$-0.183149\pi$
$89$	15.8300	1.67797	0.838986	+	0.544152i	$0.183149\pi$
$90$	6.86609	0.723750
$91$	−5.29288	−0.554844
$92$	4.28064	0.446287
$93$	−2.47133	−0.256265
$94$	−26.2453	−2.70699
$95$	6.54895	0.671908
$96$	3.01060	0.307268
$97$	3.71639	0.377342	0.188671	−	0.982040i	$-0.439582\pi$
$97$	3.71639	0.377342	0.188671	+	0.982040i	$0.439582\pi$
$98$	11.5923	1.17100
$99$	−1.30482	−0.131139
$100$	10.7278	1.07278
$101$	−0.0279137	−0.00277752	−0.00138876	−	0.999999i	$-0.500442\pi$
$101$	−0.0279137	−0.00277752	−0.00138876	+	0.999999i	$0.500442\pi$
$102$	−5.71555	−0.565923
$103$	−3.31676	−0.326810	−0.163405	−	0.986559i	$-0.552248\pi$
$103$	−3.31676	−0.326810	−0.163405	+	0.986559i	$0.552248\pi$
$104$	−19.6324	−1.92511
$105$	−4.22167	−0.411992
$106$	1.76257	0.171196
$107$	0.970450	0.0938170	0.0469085	−	0.998899i	$-0.485063\pi$
$107$	0.970450	0.0938170	0.0469085	+	0.998899i	$0.485063\pi$
$108$	−4.28064	−0.411904
$109$	5.57666	0.534148	0.267074	−	0.963676i	$-0.413943\pi$
$109$	5.57666	0.534148	0.267074	+	0.963676i	$0.413943\pi$
$110$	−8.95901	−0.854208
$111$	−10.3035	−0.977963
$112$	−8.87958	−0.839042
$113$	−1.30663	−0.122918	−0.0614588	−	0.998110i	$-0.519575\pi$
$113$	−1.30663	−0.122918	−0.0614588	+	0.998110i	$0.519575\pi$
$114$	−5.99053	−0.561065
$115$	−2.73973	−0.255481
$116$	4.28064	0.397447
$117$	3.43491	0.317558
$118$	37.3800	3.44111
$119$	3.51425	0.322150
$120$	−15.6591	−1.42947
$121$	−9.29745	−0.845223
$122$	0.164792	0.0149196
$123$	3.81467	0.343957
$124$	10.5789	0.950011
$125$	6.83256	0.611123
$126$	3.86170	0.344027
$127$	−4.65246	−0.412839	−0.206420	−	0.978464i	$-0.566181\pi$
$127$	−4.65246	−0.412839	−0.206420	+	0.978464i	$0.566181\pi$
$128$	15.9961	1.41387
$129$	−4.29040	−0.377749
$130$	23.5844	2.06849
$131$	−13.3386	−1.16540	−0.582702	−	0.812686i	$-0.698004\pi$
$131$	−13.3386	−1.16540	−0.582702	+	0.812686i	$0.698004\pi$
$132$	5.58545	0.486151
$133$	3.68332	0.319385
$134$	1.25328	0.108267
$135$	2.73973	0.235798
$136$	13.0351	1.11775
$137$	−8.53689	−0.729356	−0.364678	−	0.931134i	$-0.618821\pi$
$137$	−8.53689	−0.729356	−0.364678	+	0.931134i	$0.618821\pi$
$138$	2.50612	0.213335
$139$	−6.25654	−0.530673	−0.265336	−	0.964156i	$-0.585483\pi$
$139$	−6.25654	−0.530673	−0.265336	+	0.964156i	$0.585483\pi$
$140$	18.0714	1.52731
$141$	−10.4725	−0.881941
$142$	1.05927	0.0888916
$143$	−4.48194	−0.374798
$144$	5.76257	0.480214
$145$	−2.73973	−0.227522
$146$	−27.8265	−2.30294
$147$	4.62561	0.381514
$148$	44.1054	3.62545
$149$	−3.96274	−0.324640	−0.162320	−	0.986738i	$-0.551898\pi$
$149$	−3.96274	−0.324640	−0.162320	+	0.986738i	$0.551898\pi$
$150$	6.28064	0.512812
$151$	−6.48861	−0.528036	−0.264018	−	0.964518i	$-0.585048\pi$
$151$	−6.48861	−0.528036	−0.264018	+	0.964518i	$0.585048\pi$
$152$	13.6622	1.10815
$153$	−2.28064	−0.184378
$154$	−5.03881	−0.406039
$155$	−6.77079	−0.543843
$156$	−14.7036	−1.17723
$157$	−13.1793	−1.05183	−0.525913	−	0.850539i	$-0.676276\pi$
$157$	−13.1793	−1.05183	−0.525913	+	0.850539i	$0.676276\pi$
$158$	6.59110	0.524360
$159$	0.703308	0.0557759
$160$	8.24824	0.652081
$161$	−1.54091	−0.121440
$162$	−2.50612	−0.196899
$163$	−25.3241	−1.98354	−0.991770	−	0.128033i	$-0.959134\pi$
$163$	−25.3241	−1.98354	−0.991770	+	0.128033i	$0.959134\pi$
$164$	−16.3292	−1.27510
$165$	−3.57485	−0.278302
$166$	−39.9782	−3.10291
$167$	−6.97623	−0.539837	−0.269918	−	0.962883i	$-0.586997\pi$
$167$	−6.97623	−0.539837	−0.269918	+	0.962883i	$0.586997\pi$
$168$	−8.80712	−0.679484
$169$	−1.20139	−0.0924144
$170$	−15.6591	−1.20099
$171$	−2.39036	−0.182796
$172$	18.3656	1.40037
$173$	9.39066	0.713959	0.356979	−	0.934112i	$-0.383807\pi$
$173$	9.39066	0.713959	0.356979	+	0.934112i	$0.383807\pi$
$174$	2.50612	0.189988
$175$	−3.86170	−0.291917
$176$	−7.51911	−0.566775
$177$	14.9155	1.12112
$178$	−39.6718	−2.97353
$179$	14.0140	1.04745	0.523726	−	0.851887i	$-0.324542\pi$
$179$	14.0140	1.04745	0.523726	+	0.851887i	$0.324542\pi$
$180$	−11.7278	−0.874138
$181$	11.7427	0.872828	0.436414	−	0.899746i	$-0.356248\pi$
$181$	11.7427	0.872828	0.436414	+	0.899746i	$0.356248\pi$
$182$	13.2646	0.983236
$183$	0.0657559	0.00486082
$184$	−5.71555	−0.421356
$185$	−28.2287	−2.07542
$186$	6.19346	0.454126
$187$	2.97582	0.217613
$188$	44.8288	3.26948
$189$	1.54091	0.112084
$190$	−16.4124	−1.19068
$191$	−25.1512	−1.81988	−0.909939	−	0.414741i	$-0.863872\pi$
$191$	−25.1512	−1.81988	−0.909939	+	0.414741i	$0.863872\pi$
$192$	3.98021	0.287247
$193$	3.76994	0.271367	0.135683	−	0.990752i	$-0.456677\pi$
$193$	3.76994	0.271367	0.135683	+	0.990752i	$0.456677\pi$
$194$	−9.31371	−0.668686
$195$	9.41073	0.673916
$196$	−19.8005	−1.41432
$197$	−13.9870	−0.996532	−0.498266	−	0.867024i	$-0.666030\pi$
$197$	−13.9870	−0.996532	−0.498266	+	0.867024i	$0.666030\pi$
$198$	3.27003	0.232391
$199$	3.46558	0.245669	0.122834	−	0.992427i	$-0.460802\pi$
$199$	3.46558	0.245669	0.122834	+	0.992427i	$0.460802\pi$
$200$	−14.3238	−1.01285
$201$	0.500088	0.0352735
$202$	0.0699551	0.00492202
$203$	−1.54091	−0.108150
$204$	9.76257	0.683517
$205$	10.4512	0.729941
$206$	8.31220	0.579139
$207$	1.00000	0.0695048
$208$	19.7939	1.37246
$209$	3.11899	0.215745
$210$	10.5800	0.730090
$211$	4.25674	0.293046	0.146523	−	0.989207i	$-0.453192\pi$
$211$	4.25674	0.293046	0.146523	+	0.989207i	$0.453192\pi$
$212$	−3.01060	−0.206769
$213$	0.422671	0.0289610
$214$	−2.43206	−0.166253
$215$	−11.7545	−0.801652
$216$	5.71555	0.388894
$217$	−3.80809	−0.258510
$218$	−13.9758	−0.946560
$219$	−11.1034	−0.750300
$220$	15.3026	1.03170
$221$	−7.83378	−0.526957
$222$	25.8218	1.73304
$223$	−22.6777	−1.51861	−0.759306	−	0.650734i	$-0.774461\pi$
$223$	−22.6777	−1.51861	−0.759306	+	0.650734i	$0.774461\pi$
$224$	4.63906	0.309960
$225$	2.50612	0.167075
$226$	3.27457	0.217821
$227$	−17.9337	−1.19030	−0.595149	−	0.803615i	$-0.702907\pi$
$227$	−17.9337	−1.19030	−0.595149	+	0.803615i	$0.702907\pi$
$228$	10.2323	0.677649
$229$	0.181131	0.0119695	0.00598475	−	0.999982i	$-0.498095\pi$
$229$	0.181131	0.0119695	0.00598475	+	0.999982i	$0.498095\pi$
$230$	6.86609	0.452737
$231$	−2.01060	−0.132288
$232$	−5.71555	−0.375244
$233$	−24.6936	−1.61773	−0.808865	−	0.587994i	$-0.799918\pi$
$233$	−24.6936	−1.61773	−0.808865	+	0.587994i	$0.799918\pi$
$234$	−8.60830	−0.562742
$235$	−28.6917	−1.87164
$236$	−63.8479	−4.15614
$237$	2.63000	0.170837
$238$	−8.80712	−0.570881
$239$	1.31609	0.0851306	0.0425653	−	0.999094i	$-0.486447\pi$
$239$	1.31609	0.0851306	0.0425653	+	0.999094i	$0.486447\pi$
$240$	15.7879	1.01910
$241$	−2.66488	−0.171660	−0.0858299	−	0.996310i	$-0.527354\pi$
$241$	−2.66488	−0.171660	−0.0858299	+	0.996310i	$0.527354\pi$
$242$	23.3005	1.49781
$243$	−1.00000	−0.0641500
$244$	−0.281477	−0.0180197
$245$	12.6729	0.809643
$246$	−9.56002	−0.609525
$247$	−8.21068	−0.522433
$248$	−14.1250	−0.896940
$249$	−15.9522	−1.01093
$250$	−17.1232	−1.08297
$251$	13.6009	0.858483	0.429241	−	0.903190i	$-0.358781\pi$
$251$	13.6009	0.858483	0.429241	+	0.903190i	$0.358781\pi$
$252$	−6.59606	−0.415513
$253$	−1.30482	−0.0820333
$254$	11.6596	0.731590
$255$	−6.24833	−0.391285
$256$	−32.1277	−2.00798
$257$	−16.1780	−1.00915	−0.504577	−	0.863367i	$-0.668352\pi$
$257$	−16.1780	−1.00915	−0.504577	+	0.863367i	$0.668352\pi$
$258$	10.7523	0.669406
$259$	−15.8767	−0.986530
$260$	−40.2839	−2.49830
$261$	1.00000	0.0618984
$262$	33.4282	2.06520
$263$	16.1452	0.995557	0.497778	−	0.867304i	$-0.334149\pi$
$263$	16.1452	0.995557	0.497778	+	0.867304i	$0.334149\pi$
$264$	−7.45775	−0.458993
$265$	1.92687	0.118367
$266$	−9.23085	−0.565980
$267$	−15.8300	−0.968778
$268$	−2.14070	−0.130764
$269$	−0.348955	−0.0212762	−0.0106381	−	0.999943i	$-0.503386\pi$
$269$	−0.348955	−0.0212762	−0.0106381	+	0.999943i	$0.503386\pi$
$270$	−6.86609	−0.417857
$271$	−11.2443	−0.683043	−0.341522	−	0.939874i	$-0.610942\pi$
$271$	−11.2443	−0.683043	−0.341522	+	0.939874i	$0.610942\pi$
$272$	−13.1423	−0.796871
$273$	5.29288	0.320339
$274$	21.3945	1.29249
$275$	−3.27003	−0.197190
$276$	−4.28064	−0.257664
$277$	−32.0388	−1.92503	−0.962513	−	0.271234i	$-0.912568\pi$
$277$	−32.0388	−1.92503	−0.962513	+	0.271234i	$0.912568\pi$
$278$	15.6796	0.940402
$279$	2.47133	0.147955
$280$	−24.1291	−1.44199
$281$	9.77595	0.583184	0.291592	−	0.956543i	$-0.405815\pi$
$281$	9.77595	0.583184	0.291592	+	0.956543i	$0.405815\pi$
$282$	26.2453	1.56288
$283$	4.40306	0.261735	0.130867	−	0.991400i	$-0.458224\pi$
$283$	4.40306	0.261735	0.130867	+	0.991400i	$0.458224\pi$
$284$	−1.80930	−0.107362
$285$	−6.54895	−0.387926
$286$	11.2323	0.664178
$287$	5.87805	0.346970
$288$	−3.01060	−0.177402
$289$	−11.7987	−0.694041
$290$	6.86609	0.403191
$291$	−3.71639	−0.217859
$292$	47.5298	2.78147
$293$	6.34380	0.370609	0.185305	−	0.982681i	$-0.440673\pi$
$293$	6.34380	0.370609	0.185305	+	0.982681i	$0.440673\pi$
$294$	−11.5923	−0.676078
$295$	40.8645	2.37922
$296$	−58.8900	−3.42291
$297$	1.30482	0.0757133
$298$	9.93109	0.575293
$299$	3.43491	0.198646
$300$	−10.7278	−0.619369
$301$	−6.61110	−0.381058
$302$	16.2612	0.935729
$303$	0.0279137	0.00160360
$304$	−13.7746	−0.790030
$305$	0.180154	0.0103156
$306$	5.71555	0.326736
$307$	−18.1678	−1.03689	−0.518447	−	0.855110i	$-0.673490\pi$
$307$	−18.1678	−1.03689	−0.518447	+	0.855110i	$0.673490\pi$
$308$	8.60666	0.490410
$309$	3.31676	0.188684
$310$	16.9684	0.963740
$311$	15.5142	0.879727	0.439864	−	0.898065i	$-0.355027\pi$
$311$	15.5142	0.879727	0.439864	+	0.898065i	$0.355027\pi$
$312$	19.6324	1.11147
$313$	−27.5360	−1.55642	−0.778212	−	0.628001i	$-0.783873\pi$
$313$	−27.5360	−1.55642	−0.778212	+	0.628001i	$0.783873\pi$
$314$	33.0290	1.86393
$315$	4.22167	0.237864
$316$	−11.2581	−0.633317
$317$	−2.20692	−0.123953	−0.0619765	−	0.998078i	$-0.519740\pi$
$317$	−2.20692	−0.123953	−0.0619765	+	0.998078i	$0.519740\pi$
$318$	−1.76257	−0.0988402
$319$	−1.30482	−0.0730558
$320$	10.9047	0.609592
$321$	−0.970450	−0.0541653
$322$	3.86170	0.215204
$323$	5.45155	0.303332
$324$	4.28064	0.237813
$325$	8.60830	0.477502
$326$	63.4653	3.51502
$327$	−5.57666	−0.308390
$328$	21.8029	1.20387
$329$	−16.1371	−0.889667
$330$	8.95901	0.493177
$331$	−12.6766	−0.696770	−0.348385	−	0.937352i	$-0.613270\pi$
$331$	−12.6766	−0.696770	−0.348385	+	0.937352i	$0.613270\pi$
$332$	68.2856	3.74766
$333$	10.3035	0.564627
$334$	17.4833	0.956642
$335$	1.37011	0.0748569
$336$	8.87958	0.484421
$337$	18.5875	1.01253	0.506264	−	0.862379i	$-0.331026\pi$
$337$	18.5875	1.01253	0.506264	+	0.862379i	$0.331026\pi$
$338$	3.01082	0.163767
$339$	1.30663	0.0709665
$340$	26.7468	1.45055
$341$	−3.22464	−0.174624
$342$	5.99053	0.323931
$343$	17.9140	0.967264
$344$	−24.5220	−1.32214
$345$	2.73973	0.147502
$346$	−23.5341	−1.26520
$347$	−5.50028	−0.295271	−0.147635	−	0.989042i	$-0.547166\pi$
$347$	−5.50028	−0.295271	−0.147635	+	0.989042i	$0.547166\pi$
$348$	−4.28064	−0.229466
$349$	18.0812	0.967863	0.483931	−	0.875106i	$-0.339208\pi$
$349$	18.0812	0.967863	0.483931	+	0.875106i	$0.339208\pi$
$350$	9.67787	0.517304
$351$	−3.43491	−0.183342
$352$	3.92829	0.209379
$353$	−0.598193	−0.0318386	−0.0159193	−	0.999873i	$-0.505067\pi$
$353$	−0.598193	−0.0318386	−0.0159193	+	0.999873i	$0.505067\pi$
$354$	−37.3800	−1.98673
$355$	1.15801	0.0614606
$356$	67.7623	3.59140
$357$	−3.51425	−0.185994
$358$	−35.1206	−1.85618
$359$	−5.43779	−0.286996	−0.143498	−	0.989651i	$-0.545835\pi$
$359$	−5.43779	−0.286996	−0.143498	+	0.989651i	$0.545835\pi$
$360$	15.6591	0.825305
$361$	−13.2862	−0.699272
$362$	−29.4286	−1.54673
$363$	9.29745	0.487989
$364$	−22.6569	−1.18754
$365$	−30.4204	−1.59228
$366$	−0.164792	−0.00861383
$367$	−12.9691	−0.676984	−0.338492	−	0.940969i	$-0.609917\pi$
$367$	−12.9691	−0.676984	−0.338492	+	0.940969i	$0.609917\pi$
$368$	5.76257	0.300395
$369$	−3.81467	−0.198584
$370$	70.7446	3.67784
$371$	1.08373	0.0562645
$372$	−10.5789	−0.548489
$373$	−3.85806	−0.199763	−0.0998815	−	0.994999i	$-0.531846\pi$
$373$	−3.85806	−0.199763	−0.0998815	+	0.994999i	$0.531846\pi$
$374$	−7.45775	−0.385631
$375$	−6.83256	−0.352832
$376$	−59.8559	−3.08683
$377$	3.43491	0.176907
$378$	−3.86170	−0.198624
$379$	12.5992	0.647180	0.323590	−	0.946197i	$-0.395110\pi$
$379$	12.5992	0.647180	0.323590	+	0.946197i	$0.395110\pi$
$380$	28.0337	1.43810
$381$	4.65246	0.238353
$382$	63.0320	3.22500
$383$	−3.18743	−0.162870	−0.0814349	−	0.996679i	$-0.525950\pi$
$383$	−3.18743	−0.162870	−0.0814349	+	0.996679i	$0.525950\pi$
$384$	−15.9961	−0.816297
$385$	−5.50851	−0.280740
$386$	−9.44793	−0.480887
$387$	4.29040	0.218093
$388$	15.9085	0.807632
$389$	−37.9270	−1.92298	−0.961488	−	0.274849i	$-0.911372\pi$
$389$	−37.9270	−1.92298	−0.961488	+	0.274849i	$0.911372\pi$
$390$	−23.5844	−1.19424
$391$	−2.28064	−0.115337
$392$	26.4379	1.33531
$393$	13.3386	0.672846
$394$	35.0531	1.76595
$395$	7.20550	0.362548
$396$	−5.58545	−0.280680
$397$	10.4782	0.525886	0.262943	−	0.964811i	$-0.415307\pi$
$397$	10.4782	0.525886	0.262943	+	0.964811i	$0.415307\pi$
$398$	−8.68517	−0.435348
$399$	−3.68332	−0.184397
$400$	14.4417	0.722085
$401$	15.9163	0.794822	0.397411	−	0.917641i	$-0.369909\pi$
$401$	15.9163	0.794822	0.397411	+	0.917641i	$0.369909\pi$
$402$	−1.25328	−0.0625080
$403$	8.48881	0.422858
$404$	−0.119488	−0.00594477
$405$	−2.73973	−0.136138
$406$	3.86170	0.191653
$407$	−13.4442	−0.666403
$408$	−13.0351	−0.645333
$409$	8.90182	0.440167	0.220083	−	0.975481i	$-0.429367\pi$
$409$	8.90182	0.440167	0.220083	+	0.975481i	$0.429367\pi$
$410$	−26.1919	−1.29352
$411$	8.53689	0.421094
$412$	−14.1979	−0.699478
$413$	22.9834	1.13094
$414$	−2.50612	−0.123169
$415$	−43.7048	−2.14538
$416$	−10.3412	−0.507017
$417$	6.25654	0.306384
$418$	−7.81656	−0.382321
$419$	12.9512	0.632706	0.316353	−	0.948641i	$-0.397542\pi$
$419$	12.9512	0.632706	0.316353	+	0.948641i	$0.397542\pi$
$420$	−18.0714	−0.881795
$421$	2.12359	0.103497	0.0517487	−	0.998660i	$-0.483521\pi$
$421$	2.12359	0.103497	0.0517487	+	0.998660i	$0.483521\pi$
$422$	−10.6679	−0.519305
$423$	10.4725	0.509189
$424$	4.01979	0.195218
$425$	−5.71555	−0.277245
$426$	−1.05927	−0.0513216
$427$	0.101324	0.00490340
$428$	4.15415	0.200798
$429$	4.48194	0.216390
$430$	29.4583	1.42060
$431$	−26.2219	−1.26306	−0.631532	−	0.775349i	$-0.717574\pi$
$431$	−26.2219	−1.26306	−0.631532	+	0.775349i	$0.717574\pi$
$432$	−5.76257	−0.277252
$433$	17.6826	0.849771	0.424885	−	0.905247i	$-0.360314\pi$
$433$	17.6826	0.849771	0.424885	+	0.905247i	$0.360314\pi$
$434$	9.54354	0.458104
$435$	2.73973	0.131360
$436$	23.8717	1.14325
$437$	−2.39036	−0.114347
$438$	27.8265	1.32960
$439$	−12.0888	−0.576967	−0.288484	−	0.957485i	$-0.593151\pi$
$439$	−12.0888	−0.576967	−0.288484	+	0.957485i	$0.593151\pi$
$440$	−20.4322	−0.974068
$441$	−4.62561	−0.220267
$442$	19.6324	0.933818
$443$	21.3112	1.01253	0.506264	−	0.862379i	$-0.331026\pi$
$443$	21.3112	1.01253	0.506264	+	0.862379i	$0.331026\pi$
$444$	−44.1054	−2.09315
$445$	−43.3698	−2.05593
$446$	56.8330	2.69112
$447$	3.96274	0.187431
$448$	6.13313	0.289763
$449$	6.48212	0.305910	0.152955	−	0.988233i	$-0.451121\pi$
$449$	6.48212	0.305910	0.152955	+	0.988233i	$0.451121\pi$
$450$	−6.28064	−0.296072
$451$	4.97745	0.234379
$452$	−5.59321	−0.263083
$453$	6.48861	0.304862
$454$	44.9439	2.10932
$455$	14.5010	0.679820
$456$	−13.6622	−0.639792
$457$	−11.5228	−0.539012	−0.269506	−	0.962999i	$-0.586860\pi$
$457$	−11.5228	−0.539012	−0.269506	+	0.962999i	$0.586860\pi$
$458$	−0.453937	−0.0212111
$459$	2.28064	0.106451
$460$	−11.7278	−0.546811
$461$	41.6112	1.93803	0.969013	−	0.247010i	$-0.0794480\pi$
$461$	41.6112	1.93803	0.969013	+	0.247010i	$0.0794480\pi$
$462$	5.03881	0.234427
$463$	3.04216	0.141381	0.0706906	−	0.997498i	$-0.477480\pi$
$463$	3.04216	0.141381	0.0706906	+	0.997498i	$0.477480\pi$
$464$	5.76257	0.267521
$465$	6.77079	0.313988
$466$	61.8851	2.86677
$467$	−16.7837	−0.776657	−0.388328	−	0.921521i	$-0.626947\pi$
$467$	−16.7837	−0.776657	−0.388328	+	0.921521i	$0.626947\pi$
$468$	14.7036	0.679674
$469$	0.770589	0.0355825
$470$	71.9049	3.31673
$471$	13.1793	0.607272
$472$	85.2503	3.92396
$473$	−5.59819	−0.257405
$474$	−6.59110	−0.302739
$475$	−5.99053	−0.274865
$476$	15.0432	0.689504
$477$	−0.703308	−0.0322022
$478$	−3.29827	−0.150859
$479$	8.59016	0.392494	0.196247	−	0.980554i	$-0.437125\pi$
$479$	8.59016	0.392494	0.196247	+	0.980554i	$0.437125\pi$
$480$	−8.24824	−0.376479
$481$	35.3915	1.61371
$482$	6.67850	0.304197
$483$	1.54091	0.0701137
$484$	−39.7990	−1.80904
$485$	−10.1819	−0.462336
$486$	2.50612	0.113680
$487$	17.5263	0.794192	0.397096	−	0.917777i	$-0.370018\pi$
$487$	17.5263	0.794192	0.397096	+	0.917777i	$0.370018\pi$
$488$	0.375831	0.0170131
$489$	25.3241	1.14520
$490$	−31.7598	−1.43476
$491$	−2.78790	−0.125816	−0.0629081	−	0.998019i	$-0.520037\pi$
$491$	−2.78790	−0.125816	−0.0629081	+	0.998019i	$0.520037\pi$
$492$	16.3292	0.736178
$493$	−2.28064	−0.102715
$494$	20.5769	0.925801
$495$	3.57485	0.160678
$496$	14.2412	0.639450
$497$	0.651297	0.0292147
$498$	39.9782	1.79146
$499$	−20.1875	−0.903715	−0.451857	−	0.892090i	$-0.649238\pi$
$499$	−20.1875	−0.903715	−0.451857	+	0.892090i	$0.649238\pi$
$500$	29.2477	1.30800
$501$	6.97623	0.311675
$502$	−34.0856	−1.52131
$503$	18.5368	0.826516	0.413258	−	0.910614i	$-0.364391\pi$
$503$	18.5368	0.826516	0.413258	+	0.910614i	$0.364391\pi$
$504$	8.80712	0.392300
$505$	0.0764760	0.00340314
$506$	3.27003	0.145371
$507$	1.20139	0.0533555
$508$	−19.9155	−0.883608
$509$	4.94638	0.219245	0.109622	−	0.993973i	$-0.465036\pi$
$509$	4.94638	0.219245	0.109622	+	0.993973i	$0.465036\pi$
$510$	15.6591	0.693395
$511$	−17.1093	−0.756873
$512$	48.5237	2.14446
$513$	2.39036	0.105537
$514$	40.5439	1.78832
$515$	9.08703	0.400423
$516$	−18.3656	−0.808502
$517$	−13.6647	−0.600972
$518$	39.7889	1.74822
$519$	−9.39066	−0.412204
$520$	53.7875	2.35874
$521$	−25.3305	−1.10975	−0.554876	−	0.831933i	$-0.687234\pi$
$521$	−25.3305	−1.10975	−0.554876	+	0.831933i	$0.687234\pi$
$522$	−2.50612	−0.109690
$523$	27.7478	1.21333	0.606664	−	0.794959i	$-0.292507\pi$
$523$	27.7478	1.21333	0.606664	+	0.794959i	$0.292507\pi$
$524$	−57.0979	−2.49433
$525$	3.86170	0.168538
$526$	−40.4619	−1.76422
$527$	−5.63621	−0.245517
$528$	7.51911	0.327227
$529$	1.00000	0.0434783
$530$	−4.82897	−0.209757
$531$	−14.9155	−0.647278
$532$	15.7670	0.683585
$533$	−13.1030	−0.567556
$534$	39.6718	1.71677
$535$	−2.65877	−0.114949
$536$	2.85828	0.123459
$537$	−14.0140	−0.604747
$538$	0.874524	0.0377034
$539$	6.03558	0.259971
$540$	11.7278	0.504684
$541$	19.2053	0.825702	0.412851	−	0.910799i	$-0.364533\pi$
$541$	19.2053	0.825702	0.412851	+	0.910799i	$0.364533\pi$
$542$	28.1796	1.21042
$543$	−11.7427	−0.503927
$544$	6.86609	0.294381
$545$	−15.2786	−0.654461
$546$	−13.2646	−0.567672
$547$	−20.6006	−0.880820	−0.440410	−	0.897797i	$-0.645167\pi$
$547$	−20.6006	−0.880820	−0.440410	+	0.897797i	$0.645167\pi$
$548$	−36.5433	−1.56105
$549$	−0.0657559	−0.00280640
$550$	8.19509	0.349440
$551$	−2.39036	−0.101833
$552$	5.71555	0.243270
$553$	4.05259	0.172334
$554$	80.2932	3.41133
$555$	28.2287	1.19824
$556$	−26.7820	−1.13581
$557$	35.2426	1.49328	0.746639	−	0.665229i	$-0.231666\pi$
$557$	35.2426	1.49328	0.746639	+	0.665229i	$0.231666\pi$
$558$	−6.19346	−0.262190
$559$	14.7371	0.623314
$560$	24.3277	1.02803
$561$	−2.97582	−0.125639
$562$	−24.4997	−1.03346
$563$	−20.8449	−0.878507	−0.439253	−	0.898363i	$-0.644757\pi$
$563$	−20.8449	−0.878507	−0.439253	+	0.898363i	$0.644757\pi$
$564$	−44.8288	−1.88763
$565$	3.57982	0.150604
$566$	−11.0346	−0.463819
$567$	−1.54091	−0.0647120
$568$	2.41580	0.101365
$569$	28.9690	1.21444	0.607221	−	0.794533i	$-0.292284\pi$
$569$	28.9690	1.21444	0.607221	+	0.794533i	$0.292284\pi$
$570$	16.4124	0.687442
$571$	−34.4758	−1.44277	−0.721384	−	0.692535i	$-0.756494\pi$
$571$	−34.4758	−1.44277	−0.721384	+	0.692535i	$0.756494\pi$
$572$	−19.1855	−0.802188
$573$	25.1512	1.05071
$574$	−14.7311	−0.614864
$575$	2.50612	0.104512
$576$	−3.98021	−0.165842
$577$	15.4028	0.641227	0.320613	−	0.947210i	$-0.396111\pi$
$577$	15.4028	0.641227	0.320613	+	0.947210i	$0.396111\pi$
$578$	29.5690	1.22991
$579$	−3.76994	−0.156674
$580$	−11.7278	−0.486970
$581$	−24.5809	−1.01979
$582$	9.31371	0.386066
$583$	0.917689	0.0380068
$584$	−63.4622	−2.62608
$585$	−9.41073	−0.389086
$586$	−15.8983	−0.656754
$587$	20.3345	0.839294	0.419647	−	0.907687i	$-0.362154\pi$
$587$	20.3345	0.839294	0.419647	+	0.907687i	$0.362154\pi$
$588$	19.8005	0.816561
$589$	−5.90738	−0.243409
$590$	−102.411	−4.21620
$591$	13.9870	0.575348
$592$	59.3745	2.44028
$593$	−0.213068	−0.00874965	−0.00437482	−	0.999990i	$-0.501393\pi$
$593$	−0.213068	−0.00874965	−0.00437482	+	0.999990i	$0.501393\pi$
$594$	−3.27003	−0.134171
$595$	−9.62809	−0.394713
$596$	−16.9630	−0.694833
$597$	−3.46558	−0.141837
$598$	−8.60830	−0.352019
$599$	−25.4984	−1.04184	−0.520918	−	0.853607i	$-0.674410\pi$
$599$	−25.4984	−1.04184	−0.520918	+	0.853607i	$0.674410\pi$
$600$	14.3238	0.584769
$601$	12.9760	0.529301	0.264651	−	0.964344i	$-0.414743\pi$
$601$	12.9760	0.529301	0.264651	+	0.964344i	$0.414743\pi$
$602$	16.5682	0.675270
$603$	−0.500088	−0.0203652
$604$	−27.7754	−1.13016
$605$	25.4725	1.03560
$606$	−0.0699551	−0.00284173
$607$	−12.1310	−0.492382	−0.246191	−	0.969221i	$-0.579179\pi$
$607$	−12.1310	−0.492382	−0.246191	+	0.969221i	$0.579179\pi$
$608$	7.19643	0.291854
$609$	1.54091	0.0624407
$610$	−0.451486	−0.0182801
$611$	35.9720	1.45527
$612$	−9.76257	−0.394629
$613$	10.5478	0.426022	0.213011	−	0.977050i	$-0.431673\pi$
$613$	10.5478	0.426022	0.213011	+	0.977050i	$0.431673\pi$
$614$	45.5308	1.83747
$615$	−10.4512	−0.421432
$616$	−11.4917	−0.463014
$617$	9.77913	0.393693	0.196846	−	0.980434i	$-0.436930\pi$
$617$	9.77913	0.393693	0.196846	+	0.980434i	$0.436930\pi$
$618$	−8.31220	−0.334366
$619$	−9.84498	−0.395703	−0.197852	−	0.980232i	$-0.563396\pi$
$619$	−9.84498	−0.395703	−0.197852	+	0.980232i	$0.563396\pi$
$620$	−28.9833	−1.16400
$621$	−1.00000	−0.0401286
$622$	−38.8803	−1.55896
$623$	−24.3925	−0.977264
$624$	−19.7939	−0.792391
$625$	−31.2500	−1.25000
$626$	69.0084	2.75813
$627$	−3.11899	−0.124560
$628$	−56.4159	−2.25124
$629$	−23.4985	−0.936946
$630$	−10.5800	−0.421517
$631$	−45.3495	−1.80533	−0.902667	−	0.430340i	$-0.858394\pi$
$631$	−45.3495	−1.80533	−0.902667	+	0.430340i	$0.858394\pi$
$632$	15.0319	0.597937
$633$	−4.25674	−0.169190
$634$	5.53081	0.219656
$635$	12.7465	0.505829
$636$	3.01060	0.119378
$637$	−15.8886	−0.629527
$638$	3.27003	0.129462
$639$	−0.422671	−0.0167206
$640$	−43.8250	−1.73233
$641$	−19.4724	−0.769113	−0.384556	−	0.923101i	$-0.625646\pi$
$641$	−19.4724	−0.769113	−0.384556	+	0.923101i	$0.625646\pi$
$642$	2.43206	0.0959859
$643$	26.3465	1.03900	0.519502	−	0.854469i	$-0.326117\pi$
$643$	26.3465	1.03900	0.519502	+	0.854469i	$0.326117\pi$
$644$	−6.59606	−0.259921
$645$	11.7545	0.462834
$646$	−13.6622	−0.537533
$647$	−31.5187	−1.23913	−0.619564	−	0.784946i	$-0.712691\pi$
$647$	−31.5187	−1.23913	−0.619564	+	0.784946i	$0.712691\pi$
$648$	−5.71555	−0.224528
$649$	19.4620	0.763952
$650$	−21.5734	−0.846179
$651$	3.80809	0.149251
$652$	−108.403	−4.24541
$653$	15.0575	0.589244	0.294622	−	0.955614i	$-0.404806\pi$
$653$	15.0575	0.589244	0.294622	+	0.955614i	$0.404806\pi$
$654$	13.9758	0.546497
$655$	36.5443	1.42790
$656$	−21.9823	−0.858265
$657$	11.1034	0.433186
$658$	40.4415	1.57657
$659$	17.5364	0.683122	0.341561	−	0.939860i	$-0.389044\pi$
$659$	17.5364	0.683122	0.341561	+	0.939860i	$0.389044\pi$
$660$	−15.3026	−0.595654
$661$	29.0640	1.13046	0.565230	−	0.824933i	$-0.308787\pi$
$661$	29.0640	1.13046	0.565230	+	0.824933i	$0.308787\pi$
$662$	31.7691	1.23474
$663$	7.83378	0.304239
$664$	−91.1756	−3.53830
$665$	−10.0913	−0.391324
$666$	−25.8218	−1.00057
$667$	1.00000	0.0387202
$668$	−29.8627	−1.15542
$669$	22.6777	0.876770
$670$	−3.43365	−0.132654
$671$	0.0857996	0.00331226
$672$	−4.63906	−0.178956
$673$	−24.3551	−0.938820	−0.469410	−	0.882980i	$-0.655533\pi$
$673$	−24.3551	−0.938820	−0.469410	+	0.882980i	$0.655533\pi$
$674$	−46.5826	−1.79429
$675$	−2.50612	−0.0964606
$676$	−5.14270	−0.197796
$677$	23.4269	0.900369	0.450185	−	0.892936i	$-0.351358\pi$
$677$	23.4269	0.900369	0.450185	+	0.892936i	$0.351358\pi$
$678$	−3.27457	−0.125759
$679$	−5.72661	−0.219767
$680$	−35.7126	−1.36952
$681$	17.9337	0.687219
$682$	8.08134	0.309451
$683$	3.73192	0.142798	0.0713990	−	0.997448i	$-0.477254\pi$
$683$	3.73192	0.142798	0.0713990	+	0.997448i	$0.477254\pi$
$684$	−10.2323	−0.391241
$685$	23.3888	0.893639
$686$	−44.8946	−1.71408
$687$	−0.181131	−0.00691059
$688$	24.7237	0.942583
$689$	−2.41580	−0.0920346
$690$	−6.86609	−0.261388
$691$	−40.6745	−1.54733	−0.773665	−	0.633595i	$-0.781579\pi$
$691$	−40.6745	−1.54733	−0.773665	+	0.633595i	$0.781579\pi$
$692$	40.1980	1.52810
$693$	2.01060	0.0763765
$694$	13.7844	0.523248
$695$	17.1412	0.650204
$696$	5.71555	0.216647
$697$	8.69987	0.329531
$698$	−45.3136	−1.71514
$699$	24.6936	0.933997
$700$	−16.5305	−0.624795
$701$	−14.6991	−0.555177	−0.277588	−	0.960700i	$-0.589535\pi$
$701$	−14.6991	−0.555177	−0.277588	+	0.960700i	$0.589535\pi$
$702$	8.60830	0.324899
$703$	−24.6290	−0.928902
$704$	5.19346	0.195736
$705$	28.6917	1.08059
$706$	1.49914	0.0564210
$707$	0.0430124	0.00161765
$708$	63.8479	2.39955
$709$	22.3017	0.837558	0.418779	−	0.908088i	$-0.362458\pi$
$709$	22.3017	0.837558	0.418779	+	0.908088i	$0.362458\pi$
$710$	−2.90210	−0.108914
$711$	−2.63000	−0.0986328
$712$	−90.4769	−3.39077
$713$	2.47133	0.0925522
$714$	8.80712	0.329598
$715$	12.2793	0.459220
$716$	59.9886	2.24188
$717$	−1.31609	−0.0491502
$718$	13.6278	0.508583
$719$	6.13956	0.228967	0.114484	−	0.993425i	$-0.463479\pi$
$719$	6.13956	0.228967	0.114484	+	0.993425i	$0.463479\pi$
$720$	−15.7879	−0.588380
$721$	5.11082	0.190337
$722$	33.2967	1.23918
$723$	2.66488	0.0991078
$724$	50.2662	1.86813
$725$	2.50612	0.0930749
$726$	−23.3005	−0.864763
$727$	8.21938	0.304840	0.152420	−	0.988316i	$-0.451293\pi$
$727$	8.21938	0.304840	0.152420	+	0.988316i	$0.451293\pi$
$728$	30.2517	1.12120
$729$	1.00000	0.0370370
$730$	76.2372	2.82166
$731$	−9.78484	−0.361905
$732$	0.281477	0.0104037
$733$	−30.0927	−1.11150	−0.555750	−	0.831349i	$-0.687569\pi$
$733$	−30.0927	−1.11150	−0.555750	+	0.831349i	$0.687569\pi$
$734$	32.5022	1.19968
$735$	−12.6729	−0.467448
$736$	−3.01060	−0.110972
$737$	0.652525	0.0240361
$738$	9.56002	0.351909
$739$	−8.66756	−0.318841	−0.159421	−	0.987211i	$-0.550963\pi$
$739$	−8.66756	−0.318841	−0.159421	+	0.987211i	$0.550963\pi$
$740$	−120.837	−4.44206
$741$	8.21068	0.301627
$742$	−2.71596	−0.0997060
$743$	23.5733	0.864821	0.432411	−	0.901677i	$-0.357663\pi$
$743$	23.5733	0.864821	0.432411	+	0.901677i	$0.357663\pi$
$744$	14.1250	0.517848
$745$	10.8568	0.397763
$746$	9.66877	0.353999
$747$	15.9522	0.583661
$748$	12.7384	0.465762
$749$	−1.49537	−0.0546397
$750$	17.1232	0.625251
$751$	−7.07810	−0.258284	−0.129142	−	0.991626i	$-0.541222\pi$
$751$	−7.07810	−0.258284	−0.129142	+	0.991626i	$0.541222\pi$
$752$	60.3484	2.20068
$753$	−13.6009	−0.495645
$754$	−8.60830	−0.313496
$755$	17.7770	0.646973
$756$	6.59606	0.239896
$757$	40.0268	1.45480	0.727400	−	0.686214i	$-0.240729\pi$
$757$	40.0268	1.45480	0.727400	+	0.686214i	$0.240729\pi$
$758$	−31.5752	−1.14686
$759$	1.30482	0.0473619
$760$	−37.4308	−1.35776
$761$	−52.4927	−1.90286	−0.951430	−	0.307866i	$-0.900385\pi$
$761$	−52.4927	−1.90286	−0.951430	+	0.307866i	$0.900385\pi$
$762$	−11.6596	−0.422384
$763$	−8.59312	−0.311092
$764$	−107.663	−3.89512
$765$	6.24833	0.225909
$766$	7.98807	0.288621
$767$	−51.2334	−1.84993
$768$	32.1277	1.15931
$769$	4.45410	0.160619	0.0803095	−	0.996770i	$-0.474409\pi$
$769$	4.45410	0.160619	0.0803095	+	0.996770i	$0.474409\pi$
$770$	13.8050	0.497497
$771$	16.1780	0.582635
$772$	16.1378	0.580811
$773$	18.6124	0.669443	0.334721	−	0.942317i	$-0.391358\pi$
$773$	18.6124	0.669443	0.334721	+	0.942317i	$0.391358\pi$
$774$	−10.7523	−0.386482
$775$	6.19346	0.222476
$776$	−21.2412	−0.762514
$777$	15.8767	0.569573
$778$	95.0496	3.40769
$779$	9.11844	0.326702
$780$	40.2839	1.44240
$781$	0.551510	0.0197346
$782$	5.71555	0.204388
$783$	−1.00000	−0.0357371
$784$	−26.6554	−0.951979
$785$	36.1078	1.28874
$786$	−33.4282	−1.19235
$787$	40.6671	1.44963	0.724813	−	0.688946i	$-0.241926\pi$
$787$	40.6671	1.44963	0.724813	+	0.688946i	$0.241926\pi$
$788$	−59.8733	−2.13290
$789$	−16.1452	−0.574785
$790$	−18.0578	−0.642469
$791$	2.01340	0.0715881
$792$	7.45775	0.265000
$793$	−0.225866	−0.00802073
$794$	−26.2596	−0.931920
$795$	−1.92687	−0.0683391
$796$	14.8349	0.525809
$797$	3.35214	0.118739	0.0593695	−	0.998236i	$-0.481091\pi$
$797$	3.35214	0.118739	0.0593695	+	0.998236i	$0.481091\pi$
$798$	9.23085	0.326769
$799$	−23.8839	−0.844951
$800$	−7.54493	−0.266754
$801$	15.8300	0.559324
$802$	−39.8882	−1.40850
$803$	−14.4880	−0.511269
$804$	2.14070	0.0754965
$805$	4.22167	0.148794
$806$	−21.2740	−0.749344
$807$	0.348955	0.0122838
$808$	0.159542	0.00561267
$809$	−43.8960	−1.54330	−0.771651	−	0.636046i	$-0.780569\pi$
$809$	−43.8960	−1.54330	−0.771651	+	0.636046i	$0.780569\pi$
$810$	6.86609	0.241250
$811$	3.65506	0.128346	0.0641732	−	0.997939i	$-0.479559\pi$
$811$	3.65506	0.128346	0.0641732	+	0.997939i	$0.479559\pi$
$812$	−6.59606	−0.231476
$813$	11.2443	0.394355
$814$	33.6927	1.18093
$815$	69.3813	2.43032
$816$	13.1423	0.460074
$817$	−10.2556	−0.358798
$818$	−22.3090	−0.780017
$819$	−5.29288	−0.184948
$820$	44.7376	1.56231
$821$	−6.66144	−0.232486	−0.116243	−	0.993221i	$-0.537085\pi$
$821$	−6.66144	−0.232486	−0.116243	+	0.993221i	$0.537085\pi$
$822$	−21.3945	−0.746218
$823$	−42.8887	−1.49501	−0.747503	−	0.664258i	$-0.768747\pi$
$823$	−42.8887	−1.49501	−0.747503	+	0.664258i	$0.768747\pi$
$824$	18.9571	0.660402
$825$	3.27003	0.113848
$826$	−57.5991	−2.00413
$827$	−53.6110	−1.86424	−0.932119	−	0.362152i	$-0.882042\pi$
$827$	−53.6110	−1.86424	−0.932119	+	0.362152i	$0.882042\pi$
$828$	4.28064	0.148762
$829$	24.5007	0.850945	0.425473	−	0.904971i	$-0.360108\pi$
$829$	24.5007	0.850945	0.425473	+	0.904971i	$0.360108\pi$
$830$	109.529	3.80182
$831$	32.0388	1.11141
$832$	−13.6717	−0.473980
$833$	10.5493	0.365513
$834$	−15.6796	−0.542941
$835$	19.1130	0.661432
$836$	13.3513	0.461763
$837$	−2.47133	−0.0854218
$838$	−32.4572	−1.12122
$839$	−13.9703	−0.482310	−0.241155	−	0.970487i	$-0.577526\pi$
$839$	−13.9703	−0.482310	−0.241155	+	0.970487i	$0.577526\pi$
$840$	24.1291	0.832534
$841$	1.00000	0.0344828
$842$	−5.32197	−0.183407
$843$	−9.77595	−0.336702
$844$	18.2215	0.627211
$845$	3.29148	0.113230
$846$	−26.2453	−0.902331
$847$	14.3265	0.492264
$848$	−4.05286	−0.139176
$849$	−4.40306	−0.151113
$850$	14.3238	0.491304
$851$	10.3035	0.353199
$852$	1.80930	0.0619857
$853$	−52.9583	−1.81326	−0.906628	−	0.421930i	$-0.861353\pi$
$853$	−52.9583	−1.81326	−0.906628	+	0.421930i	$0.861353\pi$
$854$	−0.253929	−0.00868929
$855$	6.54895	0.223969
$856$	−5.54666	−0.189581
$857$	5.62978	0.192310	0.0961548	−	0.995366i	$-0.469346\pi$
$857$	5.62978	0.192310	0.0961548	+	0.995366i	$0.469346\pi$
$858$	−11.2323	−0.383463
$859$	−14.5237	−0.495543	−0.247772	−	0.968818i	$-0.579698\pi$
$859$	−14.5237	−0.495543	−0.247772	+	0.968818i	$0.579698\pi$
$860$	−50.3169	−1.71579
$861$	−5.87805	−0.200323
$862$	65.7152	2.23827
$863$	−34.0906	−1.16046	−0.580228	−	0.814454i	$-0.697037\pi$
$863$	−34.0906	−1.16046	−0.580228	+	0.814454i	$0.697037\pi$
$864$	3.01060	0.102423
$865$	−25.7279	−0.874774
$866$	−44.3147	−1.50587
$867$	11.7987	0.400705
$868$	−16.3011	−0.553294
$869$	3.43168	0.116412
$870$	−6.86609	−0.232782
$871$	−1.71776	−0.0582040
$872$	−31.8737	−1.07938
$873$	3.71639	0.125781
$874$	5.99053	0.202633
$875$	−10.5283	−0.355923
$876$	−47.5298	−1.60588
$877$	−38.1227	−1.28731	−0.643657	−	0.765314i	$-0.722584\pi$
$877$	−38.1227	−1.28731	−0.643657	+	0.765314i	$0.722584\pi$
$878$	30.2960	1.02244
$879$	−6.34380	−0.213971
$880$	20.6003	0.694437
$881$	15.4602	0.520867	0.260433	−	0.965492i	$-0.416135\pi$
$881$	15.4602	0.520867	0.260433	+	0.965492i	$0.416135\pi$
$882$	11.5923	0.390334
$883$	48.4095	1.62911	0.814554	−	0.580088i	$-0.196982\pi$
$883$	48.4095	1.62911	0.814554	+	0.580088i	$0.196982\pi$
$884$	−33.5336	−1.12786
$885$	−40.8645	−1.37364
$886$	−53.4085	−1.79429
$887$	−14.6449	−0.491727	−0.245864	−	0.969304i	$-0.579072\pi$
$887$	−14.6449	−0.491727	−0.245864	+	0.969304i	$0.579072\pi$
$888$	58.8900	1.97622
$889$	7.16901	0.240441
$890$	108.690	3.64330
$891$	−1.30482	−0.0437131
$892$	−97.0750	−3.25031
$893$	−25.0330	−0.837697
$894$	−9.93109	−0.332145
$895$	−38.3945	−1.28338
$896$	−24.6485	−0.823448
$897$	−3.43491	−0.114688
$898$	−16.2450	−0.542102
$899$	2.47133	0.0824236
$900$	10.7278	0.357593
$901$	1.60399	0.0534366
$902$	−12.4741	−0.415342
$903$	6.61110	0.220004
$904$	7.46811	0.248386
$905$	−32.1718	−1.06943
$906$	−16.2612	−0.540244
$907$	−7.41188	−0.246107	−0.123054	−	0.992400i	$-0.539269\pi$
$907$	−7.41188	−0.246107	−0.123054	+	0.992400i	$0.539269\pi$
$908$	−76.7675	−2.54762
$909$	−0.0279137	−0.000925839 0
$910$	−36.3414	−1.20470
$911$	−48.5281	−1.60781	−0.803904	−	0.594759i	$-0.797248\pi$
$911$	−48.5281	−1.60781	−0.803904	+	0.594759i	$0.797248\pi$
$912$	13.7746	0.456124
$913$	−20.8147	−0.688868
$914$	28.8774	0.955180
$915$	−0.180154	−0.00595569
$916$	0.775358	0.0256185
$917$	20.5536	0.678740
$918$	−5.71555	−0.188641
$919$	−19.1819	−0.632753	−0.316376	−	0.948634i	$-0.602466\pi$
$919$	−19.1819	−0.632753	−0.316376	+	0.948634i	$0.602466\pi$
$920$	15.6591	0.516264
$921$	18.1678	0.598651
$922$	−104.283	−3.43436
$923$	−1.45184	−0.0477879
$924$	−8.60666	−0.283138
$925$	25.8218	0.849014
$926$	−7.62402	−0.250541
$927$	−3.31676	−0.108937
$928$	−3.01060	−0.0988279
$929$	38.9302	1.27726	0.638629	−	0.769515i	$-0.279502\pi$
$929$	38.9302	1.27726	0.638629	+	0.769515i	$0.279502\pi$
$930$	−16.9684	−0.556416
$931$	11.0569	0.362375
$932$	−105.704	−3.46246
$933$	−15.5142	−0.507911
$934$	42.0619	1.37631
$935$	−8.15293	−0.266629
$936$	−19.6324	−0.641705
$937$	46.2552	1.51109	0.755545	−	0.655097i	$-0.227372\pi$
$937$	46.2552	1.51109	0.755545	+	0.655097i	$0.227372\pi$
$938$	−1.93119	−0.0630555
$939$	27.5360	0.898602
$940$	−122.819	−4.00591
$941$	−43.0101	−1.40209	−0.701045	−	0.713117i	$-0.747283\pi$
$941$	−43.0101	−1.40209	−0.701045	+	0.713117i	$0.747283\pi$
$942$	−33.0290	−1.07614
$943$	−3.81467	−0.124223
$944$	−85.9517	−2.79749
$945$	−4.22167	−0.137331
$946$	14.0297	0.456146
$947$	22.5579	0.733034	0.366517	−	0.930411i	$-0.380550\pi$
$947$	22.5579	0.733034	0.366517	+	0.930411i	$0.380550\pi$
$948$	11.2581	0.365646
$949$	38.1393	1.23805
$950$	15.0130	0.487086
$951$	2.20692	0.0715643
$952$	−20.0858	−0.650986
$953$	40.6257	1.31600	0.657998	−	0.753020i	$-0.271403\pi$
$953$	40.6257	1.31600	0.657998	+	0.753020i	$0.271403\pi$
$954$	1.76257	0.0570654
$955$	68.9076	2.22980
$956$	5.63369	0.182207
$957$	1.30482	0.0421788
$958$	−21.5280	−0.695537
$959$	13.1546	0.424783
$960$	−10.9047	−0.351948
$961$	−24.8925	−0.802984
$962$	−88.6954	−2.85966
$963$	0.970450	0.0312723
$964$	−11.4074	−0.367407
$965$	−10.3286	−0.332490
$966$	−3.86170	−0.124248
$967$	−1.11416	−0.0358290	−0.0179145	−	0.999840i	$-0.505703\pi$
$967$	−1.11416	−0.0358290	−0.0179145	+	0.999840i	$0.505703\pi$
$968$	53.1400	1.70798
$969$	−5.45155	−0.175129
$970$	25.5171	0.819303
$971$	14.4416	0.463454	0.231727	−	0.972781i	$-0.425562\pi$
$971$	14.4416	0.463454	0.231727	+	0.972781i	$0.425562\pi$
$972$	−4.28064	−0.137301
$973$	9.64074	0.309068
$974$	−43.9230	−1.40738
$975$	−8.60830	−0.275686
$976$	−0.378923	−0.0121290
$977$	−4.51331	−0.144394	−0.0721968	−	0.997390i	$-0.523001\pi$
$977$	−4.51331	−0.144394	−0.0721968	+	0.997390i	$0.523001\pi$
$978$	−63.4653	−2.02940
$979$	−20.6552	−0.660144
$980$	54.2481	1.73289
$981$	5.57666	0.178049
$982$	6.98681	0.222958
$983$	−8.42418	−0.268690	−0.134345	−	0.990935i	$-0.542893\pi$
$983$	−8.42418	−0.268690	−0.134345	+	0.990935i	$0.542893\pi$
$984$	−21.8029	−0.695052
$985$	38.3206	1.22100
$986$	5.71555	0.182020
$987$	16.1371	0.513649
$988$	−35.1469	−1.11817
$989$	4.29040	0.136427
$990$	−8.95901	−0.284736
$991$	−40.3559	−1.28195	−0.640974	−	0.767563i	$-0.721469\pi$
$991$	−40.3559	−1.28195	−0.640974	+	0.767563i	$0.721469\pi$
$992$	−7.44020	−0.236227
$993$	12.6766	0.402280
$994$	−1.63223	−0.0517711
$995$	−9.49477	−0.301004
$996$	−68.2856	−2.16371
$997$	−21.8586	−0.692270	−0.346135	−	0.938185i	$-0.612506\pi$
$997$	−21.8586	−0.692270	−0.346135	+	0.938185i	$0.612506\pi$
$998$	50.5922	1.60147
$999$	−10.3035	−0.325988

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.h.1.1	✓	5
3.2	odd	2		6003.2.a.h.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.h.1.1	✓	5	1.1	even	1	trivial
6003.2.a.h.1.5		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50612 q^{2} -1.00000 q^{3} +4.28064 q^{4} -2.73973 q^{5} +2.50612 q^{6} -1.54091 q^{7} -5.71555 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.50612 q^{2} -1.00000 q^{3} +4.28064 q^{4} -2.73973 q^{5} +2.50612 q^{6} -1.54091 q^{7} -5.71555 q^{8} +1.00000 q^{9} +6.86609 q^{10} -1.30482 q^{11} -4.28064 q^{12} +3.43491 q^{13} +3.86170 q^{14} +2.73973 q^{15} +5.76257 q^{16} -2.28064 q^{17} -2.50612 q^{18} -2.39036 q^{19} -11.7278 q^{20} +1.54091 q^{21} +3.27003 q^{22} +1.00000 q^{23} +5.71555 q^{24} +2.50612 q^{25} -8.60830 q^{26} -1.00000 q^{27} -6.59606 q^{28} +1.00000 q^{29} -6.86609 q^{30} +2.47133 q^{31} -3.01060 q^{32} +1.30482 q^{33} +5.71555 q^{34} +4.22167 q^{35} +4.28064 q^{36} +10.3035 q^{37} +5.99053 q^{38} -3.43491 q^{39} +15.6591 q^{40} -3.81467 q^{41} -3.86170 q^{42} +4.29040 q^{43} -5.58545 q^{44} -2.73973 q^{45} -2.50612 q^{46} +10.4725 q^{47} -5.76257 q^{48} -4.62561 q^{49} -6.28064 q^{50} +2.28064 q^{51} +14.7036 q^{52} -0.703308 q^{53} +2.50612 q^{54} +3.57485 q^{55} +8.80712 q^{56} +2.39036 q^{57} -2.50612 q^{58} -14.9155 q^{59} +11.7278 q^{60} -0.0657559 q^{61} -6.19346 q^{62} -1.54091 q^{63} -3.98021 q^{64} -9.41073 q^{65} -3.27003 q^{66} -0.500088 q^{67} -9.76257 q^{68} -1.00000 q^{69} -10.5800 q^{70} -0.422671 q^{71} -5.71555 q^{72} +11.1034 q^{73} -25.8218 q^{74} -2.50612 q^{75} -10.2323 q^{76} +2.01060 q^{77} +8.60830 q^{78} -2.63000 q^{79} -15.7879 q^{80} +1.00000 q^{81} +9.56002 q^{82} +15.9522 q^{83} +6.59606 q^{84} +6.24833 q^{85} -10.7523 q^{86} -1.00000 q^{87} +7.45775 q^{88} +15.8300 q^{89} +6.86609 q^{90} -5.29288 q^{91} +4.28064 q^{92} -2.47133 q^{93} -26.2453 q^{94} +6.54895 q^{95} +3.01060 q^{96} +3.71639 q^{97} +11.5923 q^{98} -1.30482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 5 q - 2 q^{2} - 5 q^{3} + 8 q^{4} - 3 q^{5} + 2 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} + 9 q^{10} - 8 q^{11} - 8 q^{12} + 5 q^{13} - 2 q^{14} + 3 q^{15} - 10 q^{16} + 2 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{21} + 10 q^{22} + 5 q^{23} + 3 q^{24} + 2 q^{25} - 3 q^{26} - 5 q^{27} - 14 q^{28} + 5 q^{29} - 9 q^{30} - 6 q^{31} - 8 q^{32} + 8 q^{33} + 3 q^{34} - 15 q^{35} + 8 q^{36} + 10 q^{37} - 10 q^{38} - 5 q^{39} + 26 q^{40} - 11 q^{41} + 2 q^{42} - 9 q^{43} - 16 q^{44} - 3 q^{45} - 2 q^{46} - 13 q^{47} + 10 q^{48} - 6 q^{49} - 18 q^{50} - 2 q^{51} + 12 q^{52} + q^{53} + 2 q^{54} + 13 q^{55} - 4 q^{56} + 9 q^{57} - 2 q^{58} + 6 q^{59} + 12 q^{60} + 23 q^{61} - 36 q^{62} - 5 q^{63} - q^{64} - 20 q^{65} - 10 q^{66} - 10 q^{67} - 10 q^{68} - 5 q^{69} - 16 q^{70} - 11 q^{71} - 3 q^{72} + 31 q^{73} - 18 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} + 3 q^{78} + 8 q^{79} - 8 q^{80} + 5 q^{81} + 16 q^{82} + 7 q^{83} + 14 q^{84} + 6 q^{85} - 36 q^{86} - 5 q^{87} - 3 q^{88} + 3 q^{89} + 9 q^{90} + 8 q^{91} + 8 q^{92} + 6 q^{93} - 39 q^{94} - 11 q^{95} + 8 q^{96} + 3 q^{97} + 38 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 5 * q^3 + 8 * q^4 - 3 * q^5 + 2 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 + 9 * q^10 - 8 * q^11 - 8 * q^12 + 5 * q^13 - 2 * q^14 + 3 * q^15 - 10 * q^16 + 2 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^21 + 10 * q^22 + 5 * q^23 + 3 * q^24 + 2 * q^25 - 3 * q^26 - 5 * q^27 - 14 * q^28 + 5 * q^29 - 9 * q^30 - 6 * q^31 - 8 * q^32 + 8 * q^33 + 3 * q^34 - 15 * q^35 + 8 * q^36 + 10 * q^37 - 10 * q^38 - 5 * q^39 + 26 * q^40 - 11 * q^41 + 2 * q^42 - 9 * q^43 - 16 * q^44 - 3 * q^45 - 2 * q^46 - 13 * q^47 + 10 * q^48 - 6 * q^49 - 18 * q^50 - 2 * q^51 + 12 * q^52 + q^53 + 2 * q^54 + 13 * q^55 - 4 * q^56 + 9 * q^57 - 2 * q^58 + 6 * q^59 + 12 * q^60 + 23 * q^61 - 36 * q^62 - 5 * q^63 - q^64 - 20 * q^65 - 10 * q^66 - 10 * q^67 - 10 * q^68 - 5 * q^69 - 16 * q^70 - 11 * q^71 - 3 * q^72 + 31 * q^73 - 18 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 + 3 * q^78 + 8 * q^79 - 8 * q^80 + 5 * q^81 + 16 * q^82 + 7 * q^83 + 14 * q^84 + 6 * q^85 - 36 * q^86 - 5 * q^87 - 3 * q^88 + 3 * q^89 + 9 * q^90 + 8 * q^91 + 8 * q^92 + 6 * q^93 - 39 * q^94 - 11 * q^95 + 8 * q^96 + 3 * q^97 + 38 * q^98 - 8 * q^99

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